Symplectic cohomology of compound Du Val singularities

TL;DR

This paper computes symplectic cohomology for Milnor fibres of specific compound Du Val singularities using homological mirror symmetry, revealing new conjectures about the relationship between resolutions and symplectic invariants.

Contribution

It introduces a novel computation of symplectic cohomology for certain singularities and proposes a conjecture linking small resolutions to symplectic cohomology.

Findings

Symplectic cohomology computations suggest a strong link with small resolutions.

Contact invariants distinguish contact structures on connected sums of S^2 x S^3.

New conjecture on the implications of small resolutions for symplectic cohomology.

Abstract

We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution has strong implications for the symplectic cohomology and conversely. We also use our computations to give a contact invariant of the link of the singularities and thereby distinguish many contact structures on connected sums of $S^2 \times S^3$.